The computer-aided design of an integrated circuit typically involves interconnecting various building blocks, commonly referred to as cells, which perform specified circuit functions. Such cells may correspond, for example, to particular predetermined arrangements of one or more logic gates, flip-flops, latches, etc. In order to determine if the overall circuit meets timing requirements, it is important to have accurate models of signal propagation delay through each of the cells. Other types of cell information, including, for example, output voltage slew, timing constraints such as setup and hold times, power consumption, and capacitive load, can also be modeled. Such models also help the designer optimize circuit performance while avoiding metastable conditions.
In an example of typical conventional practice, the cell propagation delay is modeled as a function of at least two independent variables, such as input voltage slew and output capacitive load. In one approach of this type, delay measurements are obtained, using circuit simulation software such as SPICE, for different values of input voltage slew and output capacitive load. The measured data points are stored in a two-dimensional (2D) table indexed by the particular input voltage slew and output capacitive load values used to obtain those data points. In order to determine the cell delay at other input voltage slew or output capacitive load values, linear interpolation between the measured data points is used.
It is also known to fit the delay measurement data to a multi-variable polynomial model. The polynomial model can then be evaluated at any input voltage slew and output capacitive load values in order to obtain the corresponding delay. Examples of polynomial modeling techniques of this type are disclosed in F. Wang et al., “Scalable Polynomial Delay Model for Logic and Physical Synthesis,” Synopsys Inc., 2000, and U.S. Pat. No. 6,272,664, entitled “System and Method for Using Scalable Polynomials to Translate a Look-Up Table Delay Model into a Memory Efficient Model,” both incorporated by reference herein. Polynomial models can also be configured to incorporate additional independent variables, such as supply voltage and temperature.
A problem with these and other known polynomial modeling techniques is that such techniques often fail to provide sufficient accuracy, particularly in those portions of a given modeling space in which certain independent variables, such as input voltage slew and output capacitive load, experience their greatest rates of change. The conventional techniques may therefore require the generation of additional measured data points, which can be a prohibitively time-consuming process in many applications.
Accordingly, a need exists for an improved polynomial modeling technique that provides a higher level of accuracy without significantly increasing the complexity of the modeling process and its associated computation and storage requirements.